Discrete Geodesics and Cellular AutomataReport as inadecuate




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1 LIF - Laboratoire d-informatique Fondamentale de Marseille 2 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique Inria Paris-Rocquencourt

Abstract : This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation—as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length.

Keywords : Discrete connection parallel transport general relativity Regge calculus





Author: Pablo Arrighi - Gilles Dowek -

Source: https://hal.archives-ouvertes.fr/



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